Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-28T14:46:39.440Z Has data issue: false hasContentIssue false
  • English
  • Français

On a summation method of S. Verblunsky†

Published online by Cambridge University Press:  24 October 2008

B. Kwee
B. Kwee
Affiliation:
University of Malaya
Get access Rights & Permissions [Opens in a new window]

Extract

Let 0 ≤ λ0 < λ1 < … < λn → ∞, and let

If as ω → ∞, we write

Suppose that

converges for σ > 0,

where τp(h) is finite for |h| < δ. If

we write

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 3 , May 1972 , pp. 499 - 503
Copyright
Copyright © Cambridge Philosophical Society 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Borwein, D.On the abscissae of summability of a Dirichlet series. J. London Math. Soc. 30 (1955), 68–71.CrossRefGoogle Scholar
(2)Guha, U. C.(γ, k)-summability of series. Pacific J. Math. 7 (1957), 1593–1602.CrossRefGoogle Scholar
(3)Hardy, G. H.Divergent series (Oxford University Press, 1949).Google Scholar
(4)Hardy, G. H. and Littlewood, J. E.The allied series of a Fourier series. Proc. London Math. Soc. (2), 24 (1925), 211–246.Google Scholar
(5)Kwee, B.On the general methods of suinmability. J. London Math. Soc. (2), 2 (1970), 23–31.CrossRefGoogle Scholar
(6)Verblunsky, S.Note on the sum of an oscillating series. Proc. Cambridge Philos. Soc. 26 (1930), 153–159.Google Scholar